List questions from probability-limit-theorems

Published on 09 Dec 2020 - 4:40

158

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$EX = 0$ and $\textrm{MGF}(t)= \infty$ for all $t>0$

Published on 31 Mar 2026 - 5:31

327

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Showing that the weak law of large numbers does not hold for some sequence of random variables

Published on 30 Mar 2026 - 17:03

59

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Proving that $X_n= 2^n 1_{(0,\frac{1}{n})}, n \geq 1 $ converges to zero in probability

Published on 10 Dec 2020 - 17:05

308

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Large deviations Exercise (Durret 2.7.6)

Published on 26 Mar 2026 - 3:10

97

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Limit distribution of a supremum

Published on 14 Dec 2020 - 18:51

45

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Distribution of $8n\operatorname{ln}(\sqrt{0.2\hat{p}} + \sqrt{0.8(1-\hat{p})} )$

Published on 16 Dec 2020 - 14:01

391

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find and prove probability of P({D1,D2,D3,...}=N)

Published on 17 Dec 2020 - 6:15

647

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use central limit theorem to find sample size

Published on 17 Dec 2020 - 23:14

174

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limits of continuous probability density function

Published on 20 Dec 2020 - 12:36

156

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Square integrable process with summable variations have SLLN

Published on 24 Dec 2020 - 20:22

104

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$\frac{1}{u_n}W_n-v_n\Rightarrow W$ implies $u_n \to +\infty$

Published on 27 Dec 2020 - 21:21

78

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Convergence a.s. from convergence in probability (Steele's book)

Published on 30 Dec 2020 - 21:15

91

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Distribution of sum of inverses with random signs

Published on 05 Jan 2021 - 21:25

199

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Convergence in distribution for random functions

Published on 08 Jan 2021 - 12:28

List Question

Some tablets of a company are refilled by a machine

$EX = 0$ and $\textrm{MGF}(t)= \infty$ for all $t>0$

Showing that the weak law of large numbers does not hold for some sequence of random variables

Proving that $X_n= 2^n 1_{(0,\frac{1}{n})}, n \geq 1 $ converges to zero in probability

Large deviations Exercise (Durret 2.7.6)

Limit distribution of a supremum

Distribution of $8n\operatorname{ln}(\sqrt{0.2\hat{p}} + \sqrt{0.8(1-\hat{p})} )$

find and prove probability of P({D1,D2,D3,...}=N)

use central limit theorem to find sample size

limits of continuous probability density function

Square integrable process with summable variations have SLLN

$\frac{1}{u_n}W_n-v_n\Rightarrow W$ implies $u_n \to +\infty$

Convergence a.s. from convergence in probability (Steele's book)

Distribution of sum of inverses with random signs

Convergence in distribution for random functions

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